Pedagogical studies of relativistic Hamiltonians

Abstract Relativistic Hamiltonians are defined as the sum of relativistic one-body ki-netic energies, two- and many-body interactions and their boost corrections.We review the calculation of the boost correction of the two-body interac-tion from commutation relations of the Poincar´e group and show that itsimportant terms can be easily understood from classical relativistic mechan-ics. The boost corrections for scalar- and vector-meson-exchange interactions,obtained from relativistic field theory, are shown to be in agreement with theresults of the classical calculation. These boost corrections are also shown tobe necessary to reproduce the known results of relativistic mean-field theories.We conclude with comments on the relativistic boost operator for the wavefunction of a nucleus. Several of the results presented in this pedagogicalarticle are known. We hope that a better understanding of relativistic Hamil-tonians and their relation to relativistic field theory is obtained by puttingthem together with a few new relations.PACS number: 21.30.+y